In one corner, we have a handful of senators in the Democratic caucus from purplish and reddish states who think that the Republican takeover of the Senate will put them in the driver's seat because Mitch McConnell will need their votes to overcome the filibuster, for example
“If the Republicans have an affirmative agenda, things they want to do, they are going to need Democratic or independent votes,” said [Maine Sen. Angus] King, who caucuses with Democrats. “I remember telling people back in Maine, everybody down here thinks they’re in charge. The reality is that anything that gets done has to have bipartisan support.”
And in the other corner we have the realities of the Senate Republican conference:
If McConnell does try to court moderate Democrats, the Kentucky Republican could lose GOP senators on his right flank, including the three who are expected to run for president — Ted Cruz of Texas, Marco Rubio of Florida and Rand Paul of Kentucky — as well as like-minded senators such as Mike Lee of Utah. It also remains to be seen how other new freshman conservatives who won their elections last week — such as Tom Cotton of Arkansas, Ben Sasse of Nebraska and Joni Ernst of Iowa — would react if their party’s leaders try to cut deals and win over Democrats.
There might be a handful of issues where McConnell could hold all these names together while still attracting the six or seven so-called "moderate" Democrats that he needs to block a filibuster, but those instances are likely to be few and far between. But many of the things that Republicans really care about—repealing Obamacare, for example—aren't issues on which they can or will compromise, even if Democrats were willing to. On those sorts of high profile issues, the only way for Republicans to get around the filibuster will be to get rid of it, or to use the reconciliation process for everything on the conservative wish list.
But even then, Republicans will still face an obstacle when it comes to actually turning anything they pass into law: The presidential veto, which requires a two-thirds supermajority to override. Senators like Joe Manchin or Angus King can talk all they want about how the filibuster gives them leverage, but even if McConnell doesn't ditch the filibuster, President Obama has the real leverage on the Democratic side, because without a two-thirds supermajority, Congress can't pass anything into law without it.